Robust and practical models describing the radiation field in heterogeneous photocatalytic systems, used in emerging environmental, photochemical and renewable energy applications, are fundamental for the further development of these technologies. The sixflux radiation absorption-scattering model (SFM) has shown to be particularly suitable for the modeling of the radiation field in solar pilot-plant photoreactors. In this study, the SFM was coupled to the Henyey-Greenstein (HG) scattering phase function in order to assemble the model with a more accurate description of the scattering phenomenon provided by this IntroductionAs an emerging environmental technology, heterogeneous photocatalysis has received increasing attention in recent years. Its promising applications in air and water remediation[1], clean fuels production [2], green products (e.g. self-cleaning surface [3]) and selective 4 synthesis of organic molecules [4] demonstrates great interest in this technology. The underlying basis of every photocatalytic reaction mechanism is the photoactivation of the semiconductor photocatalyst by absorption of photons with energy higher or equal than the catalyst band-gap. The consequent generation of electron-hole pairs produces a chain of reactions that drive simultaneous oxidation and reduction (redox) reactions.The evaluation of the radiation field and of the spatial distribution of radiation absorption in a photoreactor system, commonly described by the local volumetric rate of photon absorption (LVRPA), is therefore a crucial aspect in the development of efficient photocatalytic processes [5].The LVRPA is the photon equivalent to the concentration of reactant species and is always considered in the description of the kinetics of photochemical reactions and in the optimization of the performance of photoreactors. For instance, several methodologies have been proposed for the determination of the optimum catalyst load or reactor thickness which maximize the absorption of radiation [6,7].The estimation of the LVRPA has been a defiant task within the heterogeneous photocatalysis community, as result of the complex nature of the absorption and scattering radiation phenomenon, which in the most rigorous case is modeled by the Radiative Transfer Equation (RTE). The RTE for a medium that does not emit radiation is [8]: where I λ is the photon irradiance at λ wavelength, s is a spatial coordinate, Ω is the directional solid angle, κ λ is the absorption coefficient and σ λ the scattering coefficient. TheΩ → Ω is the scattering phase function representing the probability of a photon to be redirected by scattering from the direction Ω', in surroundings of the position s, into the direction Ω [8]. A trivial solution for the RTE cannot be achieved and a numerical method is always necessary.Although the precise modeling of the LVRPA and a better understanding of the radiationphotocatalyst-operational conditions nexus still remains a challenge, several approaches have been proposed to solve the RTE. The most rigoro...
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